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Research Papers

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation

[+] Author and Article Information
A. L. Schwab1

Laboratory for Engineering Mechanics, Delft University of Technology, Mekelweg 2, NL-2628 CD Delft, The Netherlandsa.l.schwab@tudelft.nl

J. P. Meijaard

Laboratory of Mechanical Automation and Mechatronics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, NL-7500 AE Enschede, The Netherlandsj.p.meijaard@utwente.nl

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(1), 011010 (Dec 08, 2009) (10 pages) doi:10.1115/1.4000320 History: Received October 28, 2008; Revised March 02, 2009; Published December 08, 2009; Online December 08, 2009

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger–Reissner or the three-field Hu–Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.

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References

Figures

Grahic Jump Location
Figure 3

The ten cross-sectional eigenmodes together with their dimensionless eigenfrequencies Ω for the free vibration of a completely free beam modeled by one ANCF fully parametrized element. See also Table 3.

Grahic Jump Location
Figure 4

The second bending eigenmode together with the dimensionless eigenfrequency Ω for the free vibration of a completely free beam modeled by one element for three ANCF element types: fully parametrized, elastic line approach with a Hellinger–Reissner method and elastic line approach with a Hu–Washizu method. See also Table 3.

Grahic Jump Location
Figure 5

The second bending eigenmode together with the dimensionless eigenfrequency Ω as in Fig. 4 but now for a simply supported beam. See also Table 4.

Grahic Jump Location
Figure 6

The second bending eigenmode together with the dimensionless eigenfrequency Ω as in Fig. 4 but now for a cantilevered beam. See also Table 5.

Grahic Jump Location
Figure 7

The first (double) cross-sectional eigenmode together with the dimensionless eigenfrequency Ω as in Fig. 4 but now for a cantilevered beam. See also Table 5.

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